A numerical study on time fractional Fisher equation using an extended cubic B-spline approximation

Volume 22, Issue 1, pp 85--96 http://dx.doi.org/10.22436/jmcs.022.01.08

Publication Date: July 15, 2020 Submission Date: March 30, 2020 Revision Date: April 29, 2020 Accteptance Date: May 16, 2020

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Authors

Tayyaba Akram - School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia. Muhammad Abbas - Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan. Ajmal Ali - School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.

Abstract

A new extended cubic B-spline approximation for the numerical solution of the time-fractional fisher equation is formed and examined. The given non-linear partial differential equation through substitution is converted into a linear partial differential equation through substitution, using Taylor's series expansion. The time-fractional derivative is approximated in Caputo's sense while the space dimension is calculated using a new extended cubic B-spline. The proposed numerical technique is shown to be unconditionally stable and convergent. The errors are used for measuring the accuracy of the proposed technique. The graphical and numerical results are presented to illustrate the performance of the technique.

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Keywords

• Time fractional Fisher equation
• extended cubic B-spline
• Caputo's derivative
• stability
• convergence

MSC

•  35R10
•  35R12
•  65M06
•  65M12

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